The present invention relates to a method and apparatus for open-loop testing and system identification to generate models of a system for model-based control of the system. More specifically, the present invention relates to a method of system identification of a multivariable nature using plant-friendly binary multi-frequency signals, in conjunction with multivariable parametric modeling techniques, to achieve significant time savings in testing time.
One method of characterizing the dynamics of a system is to apply perturbation signals at the input channels and measure the response of the system to these signals. The input and output signals are then processed to give an estimate of the dynamics of the system. This procedure is known as system identification.
In much of the literature and prior art on system identification, little attention has been paid to the design of the perturbation signal itself, other than to the fact that the signals should be persistently exciting. In the case of linear systems, this means that the signal should adequately span the bandwidth of the system being identified. One of the main reasons for this lack of attention has been an emphasis in the literature on system identification techniques for parametric models (e.g., a sum of exponentials fit to a step response, a continuous or discrete transfer function, a state-space representation, etc.). The main focus has been discrete transfer function models of single-input single-output (SISO), linear, time-invariant systems. Under these circumstances, there is not usually a great deal to choose among different perturbation signal designs. However, this is quite an idealized situation in many applications and, in practice, many signal design issues do arise.
For example, the theoretical requirement of persistent excitation on the input signals often clashes with practical considerations of “plant-friendliness.” In order to be plant-friendly, it is desirable for an input signal to: be as short as possible; not take actuators to limits or exceed move size restrictions; and cause minimum disruption to the controlled variables (i.e., low variance and small deviations from setpoint). It is, therefore, desirable to design a signal that strikes a reasonable compromise between being persistently exciting and plant-friendly.
An important question in most industrial applications is whether there may be signals and techniques, which minimize the time spent in data collection for system identification. When identifying a multi-input multi-output (MIMO) system, it is also desirable to obtain several statistically uncorrelated signals, thereby making it easier to separate out the various input/output relationships of the system. Also, when the purpose of the system identification exercise is to obtain a model for a model-based controller, it is desirable to identify the frequency region most relevant for closed-loop operation and design perturbation signals to excite the system primarily in this region.
Regarding time-domain identification, the use of step signals is a common practice. In addition, relevant work appeared in the 1960s and 1970s and stemmed from pseudo-random signals (i.e., deterministic signals with properties similar to those of random signals) based on shift register sequences.
The ease of generation of signals based on maximum-length binary sequences using shift register circuits has resulted in them being used in a range of applications. Other types of periodic signals have found little application so far given that they cannot be easily generated using shift register circuitry. These are referred to as multi-level pseudo-random signals (also know as m-signals). Also in the time domain, the use of non-periodic signals and non-periodic correlation has been investigated in the area of communications over the last few years.
Regarding frequency-domain identification, Perturbation Signals for System Identification edited by Keith Godfrey (1994) is a reference, which brings a significant amount of material on the subject together. However, there are no examples in which models obtained with different input signals are compared and the strengths and weaknesses of the different perturbation signal designs are emphasized. Nonetheless, the book is still useful for making the reader aware of the variety of perturbation signal design options available in the literature.
On the issue of system identification for model-based control and, more specifically, model predictive control (MPC), recent interest has emerged in the automatic control community. Step testing is often adopted in open-loop data collection for MPC modeling.
Step testing assumes that only one input channel is moved at a time. Each step move is held for a relatively long length of time. Often, each input move is held for an average of half the process settling time and a series of 15–20 moves may be executed for each input. In terms of their frequency characteristics, step signals tend to emphasize steady-state behavior and do not focus, therefore, on the closed-loop (faster) behavior. This means that a model with poor dynamic properties may be obtained. The plant testing time estimate for MPC, Ttest, may become prohibitively long for systems with long process settling time and/or large number of independent variables. For example, in a typical air separation process, Ttest may easily vary between 1 to 2 months depending on the particular process characteristics. This excessive plant testing time often translates into practical and economical infeasibility of MPC projects.
The main reason for this long testing time is the fact that step testing emphasizes the low frequency, steady-state, behavior of the process. This translates into long duration step moves. However, for the purpose of process control, the process information in the closed-loop bandwidth is the information most relevant for satisfactory controller operation. The difference between the closed-loop and open-loop bandwidths increases the faster the controller renders the closed-loop in comparison to the open-loop response.
Thus, plant testing time savings and better models for control may be obtained by focusing on models for satisfactory controller performance, as opposed to models obtained for the purpose of gaining thorough physical insight into the given process. This realization has been exploited in the present invention in the reduction of testing time.
The large number of step moves often used in step testing may also cause lengthening of a plant test. A large number of step moves is generally desired in order to minimize the effects of noise on the data, especially when a large signal-to-noise ratio (S/N) is not possible during test. Furthermore, unmeasured disturbances, environmental changes, or changes in operation mode during a test may cause one or more output responses to drift. Such drifting of output responses may require corrective action which, in turn, may lead to unwanted correlation between the input channels. This means that, later into the data collection, a set of data without correlation between the input channels involved is necessary. In other words, more data needs to be collected.
The technical issue of reducing plant testing time, while extracting the information relevant for process control in a plant-friendly manner and without compromising (and possibly improving) the quality of the obtained models, is challenging. This is the focus of the present invention.